Graphic equalizers give listeners an intuitive way to modify the frequency response of an audio signal—simply set the sliders to visually represent the desired curve and the corresponding shape of audio filter frequency response will be invoked. At least, that is the implied promise of the technology. However, the actual measured response of the equalizer can reveal some surprises. Filter inaccuracy, boost/cut asymmetry, and unexpected nulls can disappoint both the eye and the ear.
An audio graphic equalizer is a multi-band audio filter that provides tunable amplitude control at a fixed set of frequencies spaced regularly along a logarithmic scale. The operator controls the level of each band individually, in order to correct a magnitude response variation or to create one intentionally. The standard control interface for the graphic equalizer is a set of sliders arranged in parallel, so the implied behavior is that the audio response curve will match the magnitude setting at each slider position. The degree to which this is realized will be referred to herein as the accuracy of the equalizer.
Accurate equalizers can be implemented with finite impulse response (FIR) filtering techniques, but that approach incurs a severe design tradeoff between computing resources and frequency resolution. When computing resources are at a premium, it is practical to use a more efficient filtering technique, often by cascading infinite impulse response (IIR) filter sections together. A typical approach is to use one second-order IIR filter section per equalizer band, configured as a peaking equalizer, also known as a presence or bell filter. A peaking filter for an audio graphic equalizer typically provides gain or loss (attenuation) at a specific center frequency, while having unity frequency response magnitude, or 0 dB gain, at frequencies far removed from the center frequency. The composite magnitude response of the peaking equalizer sections in series has the desired general behavior for an audio graphic equalizer; that is, its magnitude at each control frequency varies according to its individual setting. However, due to the interaction between the filter bands, the overall response is generally inaccurate and quite different from the operator's expectation.
Historically, the frequency responses of graphic equalizers created by combining IIR filter sections only roughly match the operator settings. There are theoretical reasons for these mismatches to occur, mainly related to the shape of the peaking filter response and the overlap between the frequency response curves of the individual equalization filter sections. Various methods have been proposed to improve the accuracy of an equalizer built up from peaking filters. They generally rely on iterative error minimization or heuristic rules that are not guaranteed to yield an optimal solution.
By way of example, FIGS. 1, 2, and 3 illustrate the responses of several different graphic equalizer implementations across a few different control configurations. The graphic equalizer (GEQ) curves GEQ A, GEQ B, and GEQ C were measured from three different popular commercial products. GEQ D curve is for an equalizer made from second-order IIR peaking equalizer sections cascaded together with the gain of each section set directly to its corresponding control value without any attempt to compensate for the interaction among the filter sections. In the GEQ having curve GEQ D, each peaking equalizer section is realized as a biquad IIR filter.